Evolution and Quantitative Characterization of Stress and Displacement of Surrounding Rock Structure due to the Multiple Layers Backfill Mining under Loose Aquifers

Backfill mining is an important means of ensuring the high efficiency and safety of the coal mining under thin bedrock and loose aquifers. Based on the case study of Taiping Coalmine, the theoretical analysis of entropy and numerical modeling methods are adopted to establish the visualization model of temporal–spatial cube of stress and displacement induced by the multiple layers backfill mining. Moreover, the quantitative characterization and measurement framework of symmetric KL-divergence is established based on information entropy and mutual information. The results show that: (1) The non-uniformity of stress and displacement is enhanced due to the multiple layers backfill mining, showing certain fluctuation characteristics. (2) The KL-divergence of stress to displacement is slightly greater than that of displacement to stress, and the hotspot distribution law of stress–displacement related efficiency is consistent with KL-divergence. (3) The hotspots of stress entropy and the gap between stress entropy and displacement entropy in multiple layers backfill mining decrease obviously. (4) Stress plays a main role in displacement, and displacement is a linkage response to stress due to the coordinated deformation. Multiple layers backfill mining results in an enhanced correlation degree and more chaotic state between stress and displacement. The results will provide engineering geological basis for optimal design and safe production of backfill mining under loose aquifers.